We model an oversubscribed heterogeneous computing system where tasks arrive dynamically and a scheduler maps the tasks to machines for execution. The environment and workloads are based on those being investigated by the Extreme Scale Systems Center at Oak Ridge National Laboratory. Utility functions that are designed based on specifications from the system owner and users are used to create a metric for the performance of resource allocation heuristics. Each task has a time-varying utility (importance) that the enterprise will earn based on when the task successfully completes execution. We design multiple heuristics, which include a technique to drop low utility-earning tasks, to maximize the total utility that can be earned by completing tasks. The heuristics are evaluated using simulation experiments with two levels of oversubscription. The results show the benefit of having fast heuristics that account for the importance of a task and the heterogeneity of the environment when making allocation decisions in an oversubscribed environment. The ability to drop low utility-earning tasks allow the heuristics to tolerate the high oversubscription as well as earn significant utility.

The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. We develop a parallel algorithm for the VRP that combines a heuristic local search improvement procedure with integer programming. We run our parallel algorithm with as many as 129 processors and are able to quickly find high-quality solutions to standard benchmark problems. We assess the impact of parallelism by analyzing our procedure's performance under a number of different scenarios.

Abstract The R‐MAT graph generator introduced by Chakrabarti et al (Int Conf Data Mining, 2004) offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the graphs generated by R‐MAT and model the generator in terms of occupancy problems to prove results about the degree distributions of these graphs. We prove that the limiting degree distributions can be expressed as a mixture of normal distributions with means and variances that can be easily calculated from the R‐MAT parameters. Additionally, this article offers an efficient computational technique for computing the exact degree distribution and concise expressions for a number of properties of R‐MAT graphs. ©2011 Wiley Periodicals, Inc.*. NETWORKS, 2011

Abstract Utility companies typically send their meter readers out each day of the billing cycle in order to determine each customer's usage for the period. Customer churn requires the utility company to periodically remove some customer locations from its meter‐reading routes. On the other hand, the addition of new customers and locations requires the utility company to add new stops to the existing routes. A utility that does not adjust its meter‐reading routes over time can find itself with inefficient routes and, subsequently, higher meter‐reading costs. Furthermore, the utility can end up with certain billing days that require substantially larger meter‐reading resources than others. However, remedying this problem is not as simple as it may initially seem. Certain regulatory and customer service considerations can prevent the utility from shifting a customer's billing day by more than a few days in either direction. Thus, the problem of reducing the meter‐reading costs and balancing the workload can become quite difficult. We describe this Balanced Billing Cycle Vehicle Routing Problem in more detail and develop an algorithm for providing solutions to a slightly simplified version of the problem. Our algorithm uses a combination of heuristics and integer programming via a three‐stage algorithm. We discuss the performance of our procedure on a real‐world data set. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009